Today, computer aided engineering (CAE) has been used for supporting engineers in tasks such as analysis, simulation, design, manufacture, etc. In a conventional engineering design procedure, CAE analysis (e.g., finite element analysis (FEA), finite difference analysis, meshless analysis, computational fluid dynamics (CFD) analysis, modal analysis for reducing noise-vibration-harshness (NVH), etc.) has been employed to evaluate responses (e.g., stresses, displacements, etc.). Using automobile design as an example, a particular version or design of a car is analyzed using FEA to obtain the responses due to certain loading conditions. Engineers will then try to improve the car design by modifying certain parameters or design variables (e.g., thickness of the steel shell, locations of the frames, etc.) based on specific objectives and constraints. Another FEA is conducted to reflect these changes until a “best” design has been achieved. However, this approach generally depends on knowledge of the engineers or based on a trial-and-error method. To solve this problem, a systematic approach (referred to as design optimization) to identify the “best” design is used.
Traditionally, design optimization is performed with a computer system and generally divided into three categories, sizing, shape and topology. Topology optimization is best suited for creating optimal conceptual design in which the user (i.e., engineer, designer, etc.) does not have put too many constraints as to the shape and/or size of the engineering product. However, there are problems associated with topology optimization especially for the topology optimization of a component of a complex structure, where the structure responses of the complex structure or engineering product is calculated using a finite element analysis (FEA). In particular, the design variable in the topology optimization is a continuous real number, which is associated with material models in the FEA model. Difficulties for handling infinite possibilities of material models include very long, expensive and infeasible procedure to perform topology optimization. As a result, only relatively simple or simplified complex structure can be optimized using prior art approaches in topology optimization. Therefore, it would be desirable to have improved methods and systems for performing topology optimization for designing an engineering product.